We present a high-resolution elemental-abundance analysis for a sample of 23 very metal-poor (VMP; [Fe/H] < −2.0) stars, 12 of which are extremely metal-poor (EMP; [Fe/H] < −3.0), and 4 of which are ultra metal-poor (UMP; [Fe/H] < −4.0). These stars were targeted to explore differences in the abundance ratios for elements that constrain the possible astrophysical sites of element production, including Li, C, N, O, the α-elements, the iron-peak elements, and a number of neutron-capture elements. This sample substantially increases the number of known carbon-enhanced metal-poor (CEMP) and nitrogen-enhanced metal-poor (NEMP) stars -our program stars include eight that are considered "normal" metal-poor stars, six CEMP-no stars, five CEMP-s stars, two CEMP-r stars, and two CEMP-r/s stars. One of the CEMP-r stars and one of the CEMP-r/s stars are possible NEMP stars. We detect lithium for three of the six CEMP-no stars, all of which are Li-depleted with respect to the Spite plateau. The majority of the CEMP stars have [C/N] > 0. The stars with [C/N] < 0 suggest a larger degree of mixing; the few CEMP-no stars that exhibit this signature are only found at [Fe/H] < −3.4, a metallicity below which we also find the CEMP-no stars with large enhancements in Na, Mg, and Al. We confirm the existence of two plateaus in the absolute carbon abundances of CEMP stars, as suggested by Spite et al. We also present evidence for a "floor" in the absolute Ba abundances of CEMP-no stars at A(Ba) ∼ −2.0. 1 Based on observations made with the European Southern Observatory telescopes.enhanced metal-poor (CEMP) stars (Beers et al. 1992; Beers & Christlieb 2005; Norris et al. 2013b). This class comprises a number of sub-classes (originally defined by Beers & Christlieb 2005), based on the behavior of their neutron-capture elements:(1) CEMP-no stars, which exhibit no over-abundances of n-capture elements, (2) CEMP-s stars, which show n-capture over-abundances consistent with the slow neutron-capture process, (3) CEMP-r stars, with n-capture over-abundances associated with the rapid neutron-capture process, and (4) CEMP-r/s stars, which exhibit n-capture overabundances that suggest contribution from both the slow and rapid neutron-capture processes. Each of these subclasses appear to be associated with different elementproduction histories, thus their study provides insight into the variety of astrophysical sites in the early Galaxy that were primarily responsible for their origin. The CEMP-no stars are of special importance, as the preponderance of evidence points to their being associated with elemental-abundance patterns that were produced by the very first generation of massive stars (Norris et al. 2013b;Hansen et al. 2014;Maeder et al. 2014), thus they potentially provide a unique probe of the first mass function in the early universe along with providing information on the nucleosynthesis and properties of the first stars.In a previous paper, Hansen et al. (2014) (hereafter paper I) provided a detailed study of the elemental abundances f...